Dean's letter is just a formality. It just says you're a student there. Check with the school you're transferring to to find out when you need to get it/if you need to get it.

No one here is going to be able to tell you for sure what you need on a statement but in general schools say, and its probably true, that you need to talk about why you want to transfer. It should be very different from your initial PS because they know that you want to be a lawyer and they know your aptitude for the work (based on grades). You need to convince them that you are serious about transferring to their university.